Minimax estimation of a bivariate cumulative distribution function

Rafał Połoczański () and Maciej Wilczyński ()
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Rafał Połoczański: Wrocław University of Science and Technology
Maciej Wilczyński: Wrocław University of Science and Technology

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 5, No 4, 597-615

Abstract: Abstract The problem of estimating a bivariate cumulative distribution function F under the weighted squared error loss and the weighted Cramer–von Mises loss is considered. No restrictions are imposed on the unknown function F. Estimators, which are minimax among procedures being affine transformation of the bivariate empirical distribution function, are found. Then it is proved that these procedures are minimax among all decision rules. The result for the weighted squared error loss is generalized to the case where F is assumed to be a continuous cumulative distribution function. Extensions to higher dimensions are briefly discussed.

Keywords: Minimax estimation; Cumulative distribution function; Loss function (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00184-019-00747-0

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